Fast and efficient simulation of the dynamical response of coaxial magnetic gears through direct analytical torque modelling

Coaxial magnetic gears have been of great interest amongst researchers and the industry since their introduction two decades ago. Although magnetic gears suffer from slippage at high torques and in general have lower torque density compared to their mechanical counterparts, they surpass their performance in terms of attained speeds, versatility, vibration attenuation, backdrivability and efficiency. Increasing the torque density is a major issue in magnetic drivetrains that has been extensively discussed in the literature. However, the calculation of the torque is typically performed through FEA and/or numerical methods, thus increasing the computational cost especially in dynamical simulations where the applied torques at the two rotors have to be calculated at each time step. The objective of this work is to introduce an analytical 2D model for fast and efficient calculation of the applied torques for every rotation angle, geometry configuration and constitutive parameters of the magnets using the Maxwell Stress Tensor. The results obtained from the model were compared against those obtained from FEA. The calculated torques at the inner and outer rotor were in perfect agreement with FEA, however the analytical model was more than two orders of magnitude faster. In addition, an analytical calculation of the torque ripple in coaxial magnetic gear drives is made possible using the proposed model. An investigation of the influence of the modulator ring on stall torque was performed illustrating that there is an optimum length value for the ferromagnetic segment to maximize torque density. Furthermore, the motion equations of the coaxial magnetic gear drive were formulated and a model was developed to simulate the dynamical response of the system without the requirement of torque calculation at each time step that significantly decreases computational cost. The slip effect was investigated and the resulting transmission error was determined.